A uniform bar has two small balls glued to its ends. The bar is 2.00 m long and has mass 4.00 kg, while the balls each have mass 0.300 kg and can be treated as point masses. Find the moment of inertia of this combination about an axis (a) perpendicular to the bar through its center;

Video transcript

So in this problem there are two tiny balls affixed to the end of the bar. The balls can be thought of as point masses and masses of 20.0.3 kilograms each, whereas the bar is two m long and has amassed four kg. And we want to find combinations moment inertia around an access that passes through the middle of the bar and is perpendicular to the act of the bar. So we have two balls true by a rod or a bar. We want to find the moment of inertia of this entire system where the rotational axis through the center of the bar perpendicular to the entire system. So we know from this problem that the mass of each ball is equal to . kg. An empty mass. The bar is equal to four kg. That the length of the bar Is equal to two m to define the total moment. Yes, moment of inertia. We can simply just add the contributions of each mass point. So we can add the moment ownership of the bar Plus two times the moment of inertia of balls which are identical and contribution. So we were called the moment inertia of the bar where the center where the rotational axis through the center perpendicular to the bar is equal to one or 1 12 rather Times 10 times out the bar squared. And for the balls we consider them point objects from this rotational axis. So the among the inertia of the ball will just be him of the ball times are squared where r is the distance from this rotational access to one of the balls, so R is equal to two, so R is equal to one m. We can make the substitution is to now find the total moment of another show. Okay, I'm out of the bar, which is four kg. I love the bar, which is two m squared most two times, and of the ball, which is .3 kg times R squared, which is one m squared. We get the total moment of inertia of this combination is 1. kg times meters squared. Hands with choice called themselves have a great day.